A capacitor is a passive electronic component that is used to store energy in the form of an electrostatic field and comprises a pair of electrodes separated by a dielectric layer. Each of the electrodes has an area A and are separated from each other by a distance d. When a potential difference exists between two electrodes, an electric field is present in the dielectric layer. This field stores energy and an ideal capacitor is characterized by a single constant value of capacitance which is the ratio of the electric charge on each electrode to the potential difference between them. Charge may be considered to be distributed uniformly over the area A of each electrode, and a surface charge density σ for each electrode can be expressed as ±σ=±Q/A. As the width of the electrodes is much greater than the separation (distance) d, an electrical field near the center of the capacitor will be uniform with the magnitude E=ρ/ε. Voltage is defined as a line integral of the electric field between electrodes. An ideal capacitor is characterized by a constant capacitance C, defined by the formula (1)C=Q/V,  (1)
which shows that capacitance increases with area and decreases with distance. For high voltage applications much larger capacitors have to be used.
One of important characteristic of a dielectric material is its breakdown voltage Vbd. There are a number of factors that can dramatically reduce the breakdown voltage that is a breakdown of dielectric layer along electric field lines will take place. Geometry of the conductive electrodes is important for these applications. In particular, sharp edges or points hugely increase the electric field strength locally and can lead to a local breakdown. Once a local breakdown starts at any point, the breakdown will quickly “trace” through the dielectric layer till it reaches the opposite electrode and causes a short circuit.
Breakdown of the dielectric layer usually occurs as follows. Intensity of an electric field becomes high enough to “pull” electrons from atoms of the dielectric material and make them conduct an electric current from one electrode to another. Presence of impurities in the dielectric or imperfections of the crystal structure can result in an avalanche breakdown as observed in semiconductor devices.
A characteristic electric field known as the breakdown strength Ebd, is the electric field intensity at which the dielectric layer in a capacitor becomes conductive. The breakdown voltage is related to the breakdown strength by the product of dielectric strength and separation between the electrodes,Vbd=Ebdd  (2)
Another of important characteristic of a dielectric material is its dielectric permittivity ε. Different types of dielectric materials are used for capacitors and include ceramics, polymer film, paper, and electrolytic capacitors of different kinds. The most widely used polymer film materials are polypropylene and polyester. Increase of dielectric permittivity allows increasing of volumetric energy density which makes it an important technical task. The dielectric permittivity c for a material is often expressed as the product of a dimensionless dielectric constant κ and the permittivity of free space ε0 (8.85×10−12 Farads/meter). Therefore the capacitance is largest in devices made of materials of high permittivity.
The maximal volumetric energy density stored in the capacitor is proportional to ˜ε·E2bd. Thus, in order to increase the stored energy of the capacitor it is necessary to increase dielectric permittivity ε (or dielectric constant κ) and breakdown strength Ebd of the dielectric material.
An ultra-high dielectric constant composite of polyaniline, PANI-DBSA/PAA, was synthesized using in situ polymerization of aniline in an aqueous dispersion of poly-acrylic acid (PAA) in the presence of dodecylbenzene sulfonate (DBSA) (see, Chao-Hsien Hoa et al., “High dielectric constant polyaniline/poly(acrylic acid) composites prepared by in situ polymerization”, Synthetic Metals 158 (2008), pp. 630-637). The water-soluble PAA served as a polymeric stabilizer, protecting the PANI particles from macroscopic aggregation. A very high dielectric constant of ca. 2.0*105 (at 1 kHz) was obtained for the composite containing 30% PANI by weight. Influence of the PANI content on the morphological, dielectric and electrical properties of the composites was investigated. Frequency dependence of dielectric permittivity, dielectric loss, loss tangent and electric modulus were analyzed in the frequency range from 0.5 kHz to 10 MHz. SEM micrograph revealed that composites with high PANI content (i.e., 20 wt. %) consisted of numerous nano-scale PANI particles that were evenly distributed within the PAA matrix. High dielectric constants were attributed to the sum of the small capacitors of the PANI particles. The drawback of this material is a possible occurrence of percolation and formation of at least one continuous electrically conductive channel under electric field with probability of such an event increasing with an increase of the electric field. When at least one continuous electrically conductive channel (track) through the neighboring conducting PANI particles is formed between electrodes of the capacitor, it decreases a breakdown voltage of such capacitor.
Colloidal polyaniline particles stabilized with a water-soluble polymer, poly(N-vinylpyrrolidone) [poly(1-vinylpyrrolidin-2-one)], have been prepared by dispersion polymerization. The average particle size, 241±50 nm, have been determined by dynamic light scattering (see, Jaroslav Stejskal and Irina Sapurina, “Polyaniline: Thin Films and Colloidal Dispersions (IUPAC Technical Report)”, Pure and Applied Chemistry, Vol. 77, No. 5, pp. 815-826 (2005).
Single crystals of doped aniline oligomers are produced via a simple solution-based self-assembly method (see, Yue Wang, et. al., “Morphological and Dimensional Control via Hierarchical Assembly of Doped Oligoaniline Single Crystals”, J. Am. Chem. Soc. 2012, 134, pp. 9251-9262). Detailed mechanistic studies reveal that crystals of different morphologies and dimensions can be produced by a “bottom-up” hierarchical assembly where structures such as one-dimensional (1-D) nanofibers can be aggregated into higher order architectures. A large variety of crystalline nanostructures, including 1-D nanofibers and nanowires, 2-D nanoribbons and nanosheets, 3-D nanoplates, stacked sheets, nanoflowers, porous networks, hollow spheres, and twisted coils, can be obtained by controlling the nucleation of the crystals and the non-covalent interactions between the doped oligomers. These nanoscale crystals exhibit enhanced conductivity compared to their bulk counterparts as well as interesting structure-property relationships such as shape-dependent crystallinity. Furthermore, the morphology and dimension of these structures can be largely rationalized and predicted by monitoring molecule-solvent interactions via absorption studies. Using doped tetra-aniline as a model system, the results and strategies presented in this article provide insight into the general scheme of shape and size control for organic materials.
Thus, materials with high dielectric permittivity which are based on composite materials and containing polarized particles (such as PANI particles) may demonstrate a percolation phenomenon. The formed polycrystalline structure of layers has multiple tangling chemical bonds on borders between crystallites. When the used material with high dielectric permittivity possesses polycrystalline structure, a percolation may occur along the borders of crystal grains.
Hyper-electronic polarization of organic compounds is described in greater detail in Roger D. Hartman and Herbert A. Pohl, “Hyper-electronic Polarization in Macromolecular Solids”, Journal of Polymer Science: Part A-1 Vol. 6, pp. 1135-1152 (1968). Hyper-electronic polarization may be viewed as the electrical polarization external fields due to the pliant interaction with the charge pairs of excitons, in which the charges are molecularly separated and range over molecularly limited domains. In this article four polyacene quinone radical polymers were investigated. These polymers at 100 Hz had dielectric constants of 1800-2400, decreasing to about 58-100 at 100,000 Hz. An essential drawback of the described method of production of material is use of a high pressure (up to 20 kbars) for forming the samples intended for measurement of dielectric constants.
Capacitors as energy storage device have well-known advantages versus electrochemical energy storage, e.g. a battery. Compared to batteries, capacitors are able to store energy with very high power density, i.e., very high charge/recharge rates, have long shelf life with little degradation, and can be charged and discharged (cycled) hundreds of thousands or millions of times. However, conventional capacitors often do not store energy in a sufficiently small volume or weight as compared to the case of a battery, or at low energy storage cost, which makes capacitors impractical for some applications, for example electric vehicles. Accordingly, it may be an advance in energy storage technology to provide capacitors of higher volumetric and mass energy storage density and lower cost.